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A306015 Exponential series expansion of (exp(x*y) + sinh(x) - cosh(x))/(1 - x). 2
0, 1, 1, 1, 2, 1, 4, 6, 3, 1, 15, 24, 12, 4, 1, 76, 120, 60, 20, 5, 1, 455, 720, 360, 120, 30, 6, 1, 3186, 5040, 2520, 840, 210, 42, 7, 1, 25487, 40320, 20160, 6720, 1680, 336, 56, 8, 1, 229384, 362880, 181440, 60480, 15120, 3024, 504, 72, 9, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

G. C. Greubel, Rows n=0..99 of triangle, flattened

EXAMPLE

[0] 0

[1] 1, 1

[2] 1, 2, 1

[3] 4, 6, 3, 1

[4] 15, 24, 12, 4, 1

[5] 76, 120, 60, 20, 5, 1

[6] 455, 720, 360, 120, 30, 6, 1

[7] 3186, 5040, 2520, 840, 210, 42, 7, 1

[8] 25487, 40320, 20160, 6720, 1680, 336, 56, 8, 1

[9] 229384, 362880, 181440, 60480, 15120, 3024, 504, 72, 9, 1

MAPLE

gf := (exp(x*y) + sinh(x) - cosh(x))/(1 - x):

ser := series(gf, x, 16): L := [seq(n!*coeff(ser, x, n), n=0..14)]:

seq(seq(coeff(L[k+1], y, n), n=0..k), k=0..12);

MATHEMATICA

Join[{0}, With[{nmax = 15}, CoefficientList[CoefficientList[Series[ (Exp[x*y] + Sinh[x] - Cosh[x])/(1 - x), {x, 0, nmax}, {y, 0, nmax}], x], y ]*Range[0, nmax]!] // Flatten ] (* G. C. Greubel, Jul 18 2018 *)

CROSSREFS

A094587 with an extra first column A002467.

Row sums are A306150.

Sequence in context: A257640 A262930 A293387 * A171087 A105364 A180405

Adjacent sequences:  A306012 A306013 A306014 * A306016 A306017 A306018

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Jun 23 2018

STATUS

approved

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Last modified September 19 07:08 EDT 2021. Contains 347554 sequences. (Running on oeis4.)